cp's OEIS Frontend

A160818 Each number is the average of the numbers formed by all the possible permutations of the digits of that number.

%I A160818 #19 Jun 08 2021 14:57:26
%S A160818 1,2,3,4,5,6,7,8,9,11,22,33,44,55,66,77,88,99,111,222,333,370,407,444,
%T A160818 481,518,555,592,629,666,777,888,999,1111,2222,3333,4444,5555,6666,
%U A160818 7777,8888,9999,11111,22222,33333,44444,55555,66666,77777,88888,99999,111111
%N A160818 Each number is the average of the numbers formed by all the possible permutations of the digits of that number.
%C A160818 A number n with k digits and digit sum s occurs in the sequence if and only if (10^k-1)*s = 9*k*n. - _Hagen von Eitzen_, Jun 17 2009
%C A160818 Many terms (perhaps all) are related to decimal expansions of fractions with a power of 3 in the denominator (see Munafo webpage). - _Robert Munafo_, Jun 18 2009
%C A160818 Replacing "all possible permutations" in the definition with "all cyclic permutations" produces the same sequence. Even more generally, the symmetric group can be replaced by any finite group operating transitively on the n places. - _Hagen von Eitzen_, Jun 22 2009
%H A160818 H. v. Eitzen, <a href="/A160818/b160818.txt">Table of n, a(n) for n=1..1002</a>
%H A160818 Robert Munafo, <a href="http://mrob.com/pub/seq/a160818.html">Equal to Average of Permutations of its Digits</a> [From _Robert Munafo_, Jun 18 2009]
%e A160818 a(22) = 370 is a member because 073+037+307+370+703+730 = 2220, average = 2220/6 = 370
%p A160818 Lton := proc(L) add( op(i,L)*10^(i-1),i=1..nops(L)) ; end: isA160818 := proc(n) local dgs,av ; dgs := combinat[permute]( convert(n,base,10) ); av := add( Lton(p),p=dgs)/nops(dgs) ; RETURN(av=n) ; end: for n from 1 to 40000 do if isA160818(n) then printf("%d,",n) ; fi; od: # _R. J. Mathar_, May 29 2009
%o A160818 (C)  See Robert Munafo link
%o A160818 (PARI) for(k=1, 20, rep=(10^k-1)/9; for(s=1, 9*k, if((rep*s)%k==0 && A007953(n=rep*s/k)==s, print1(n, ", ")))) \\ _Hagen von Eitzen_, Jun 22 2009
%K A160818 nonn,base
%O A160818 1,2
%A A160818 _Claudio Meller_, May 27 2009
%E A160818 15 more terms from _R. J. Mathar_, May 29 2009
%E A160818 More terms from _Robert Munafo_, Jun 18 2009